math help interval notation?

Question

i have these problems ihave to work on but i cant get the answers right can someone please help problems are for interval notation

x^2+2x<15

Answer 1

x^2 + 2x - 15 < 0
Factor the LHS:
(x+5)(x-3) < 0

You have a product of two factors resulting in a negative number, so one of your two factores must be negative and the other positive. Two options:

1) x+5>0 and x-3<0 --->
x>-5 and x<3 --->
(-5,3) is the first solution.

OR

2) x+5<0 and x-3>0 --->
x<-5 and x>3 ---> impossible.

So 1) is the only possibility and your answer is the interval (-5,3).

Answer 2

x^2+2x<15
Solve for the points where x =0
x^2 +2x -15 = 0
(x+5)(x-3) = 0
x+5=0
x=-5
x-3=0
x=3
Therefore the interval is for values of x that are less than 3 and greater -5. Interval notation is -5
When x = 3 or -5 x^2 +2x =15. That is why we have x<3 and
x> -5. If you plotted the graph of X^2 + 2x -15 = 0 ,it would be a parabola that has its vertex at (-1,-16). The parabola comes downward , crosses the x- axis at (-5,0), contiues down to its minimum value at (-1, -16) tnen goes up and vrosses the x-axis at (3,0) ant continuesvonward forever.

Answer 3

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Answer 4

I will tell you how to do it:

First step -- rewrite the inequality as:

x^2+2x-15 < 0

second step -- find where the left hand side is equal to zero. You might want to use the quadratic equation for this.

Once you have the two values that make the left equal to zero (call them a and b -- where a
(-infinity, a)
(a, b)
(b, infinity)

Pick a point from each interval & plug it into the inequality. If the left side is less than zero, then that whole interval will be less than zero. If it is greater than zero, then the whole interval will be grater than zero.

You will find that the interval (a, b) is going to be less than zero.

Good luck.

Answer 5

i agree with the others